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The Cauchy problem of generalized Landau-Lifshitz equation into S n

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Abstract

In this paper, we study the Cauchy problem of an integrable evolution system, i.e., the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation. By rewriting this equation in a geometric form and applying the geometric energy method with a forth-order perturbation, we show the global well-posedness of the Cauchy problem in suitable Sobolev spaces.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Chong Song

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Jie Yu

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  1. Chong Song
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  2. Jie Yu
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Correspondence to Chong Song.

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Song, C., Yu, J. The Cauchy problem of generalized Landau-Lifshitz equation into S n . Sci. China Math. 56, 283–300 (2013). https://doi.org/10.1007/s11425-012-4484-x

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  • DOI: https://doi.org/10.1007/s11425-012-4484-x

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